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Grace [21]
3 years ago
11

BRANLIESTS GOING OUT!

Mathematics
1 answer:
AleksandrR [38]3 years ago
5 0

Answer:

Width is 2,000 and length is 2,010

Step-by-step explanation:

I went for the width first. You multiply by 2 to get the width and add 10 for the length (I'm sorry if its wrong)

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Explain the steps to finding the vertex of g(x) = 3x2 + 12x + 15
RUDIKE [14]

Answer:

The vertex of this parabola, (-2, 3), can be found by completing the square.

Step-by-step explanation:

The goal is to express this parabola in its vertex form:

g(x) = a\, (x - h)^2 + k,

where a, h, and k are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at (h,\, k).

The vertex form can be expanded to obtain:

\begin{aligned}g(x)&= a\, (x - h)^2 + k \\ &= a\, \left(x^2 - 2\, x\, h + h^2\right) + k = a\, x^2 - 2\, a\, h\, x + \left(a\,h^2 + k\right)\end{aligned}.

Compare that expression with the given equation of this parabola. The constant term, the coefficient for x, and the coefficient for x^2 should all match accordingly. That is:

\left\lbrace\begin{aligned}& a = 3 \\ & -2\,a\, h = 12 \\& a\, h^2 + k = 15\end{aligned}\right..

The first equation implies that a is equal to 3. Hence, replace the "a\!" in the second equation with 3\! to eliminate \! a:

(-2\times 3)\, h = 12.

h = -2.

Similarly, replace the "a" and the "h" in the third equation with 3 and (-2), respectively:

3 \times (-2)^2 + k = 15.

k = 3.

Therefore, g(x) = 3\, x^2 + 12\, x + 15 would be equivalent to g(x) = 3\, (x - (-2))^2 + 3. The vertex of this parabola would thus be:

\begin{aligned}&(-2, \, 3)\\ &\phantom{(}\uparrow \phantom{,\,} \uparrow \phantom{)} \\ &\phantom{(}\; h \phantom{,\,} \;\;k\end{aligned}.

8 0
3 years ago
Which expression is equivalent to -6x^3 • x • y^2 • y^6?
Georgia [21]

Use the Product Rule: x^ax^b = x^a + b

6x^3 + 1y^2 + 6

Simplify 3 + 1 to 4

6x^4y^2 + 6

Simplify 2 + 6 to 8

<u>= C) 6x^4 y^8</u>

4 0
3 years ago
How do you know what to split 26 into ?
madam [21]

Answer:

see explanation

Step-by-step explanation:

Assuming you are factoring the expression

Given

4y² + 26y + 30 ← factor out 2 from each term

= 2(2y² + 13y + 15) ← factor the quadratic

Consider the factors of the product of the coefficient of the y² term and the constant term which sum to give the coefficient of the y- term.

product = 2 × 15 = 30 and sum = 13

the factors are 10 and 3

Use these factors to split the y- term

2y² + 10y + 3y + 15 ( factor the first/second and third/fourth terms )

= 2y(y + 5) + 3(y + 5) ← factor out (y + 5) from each term

= (y + 5)(2y + 3)

Thus

4y² + 26y + 30

= 2(y + 5)(2y + 3)

5 0
3 years ago
Which word best describes the range of a function?
cluponka [151]
The answer to the question is D
7 0
3 years ago
Read 2 more answers
Ida wants to buy a car. She borrows $2500 at an interest rate of 4% and pay the total off after 12 months. What is the amount of
katen-ka-za [31]

Answer:2600

Step-by-step explanation:

4 0
3 years ago
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